My guess is that you may have some 3rd party app installed that's draining it. I had that issue before, but not knowing what it was I reinstalled the firmware from scratch and no more battery drain. Disabling WiFi also helps me quite a bit, but I've noticed at home it's not an issue but only on other people's routers. Also, a lot of texting kills the battery I've noticed.
USB supplies 5v of power, which range from about 4.75v to 5.25v so you should be fine as that isn't going to fry your battery. Higher than that then I would worry.
Older chargers only carry about 500mA, while the newer ones for the past several years will carry 1A of current. Cheaper chargers may be even less which relates into a slower charge.
If you just bought the iPod on Friday, I'd take it back to the store if you're that concerned about the battery life. Well, make an appointment with Apple THEN go to the store, otherwise they won't even talk to you.